Actually, I have suddenly found an increase in a number of backlinks and decrease in my SEO rankings.

I checked all these new sites from where I gained the links, but cannot find my website URL when I used View Source option (Ctrl + U)

So is it possible that my website's URL is included in the Javascript and Google is counting them as backlinks and they are classified in toxic backlinks? However, I haven't received any notification in webmasters.

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As indicated in the linked question, backlinks are links, not URLs. You can simply request the JavaScript file you want to look at in your browser to view its source code, or use its Developer Tools. You can't really control which site links to yours, but you can disavow them - see Google's help doc on how to disavow backlinks.
– dan♦Sep 18 '17 at 3:18